RAIN falling from a black sky. Drumbeats pulsing. People running through woods. The third and final series of The Killing arrives on BBC4 on Saturday night – and it already looks like it will dominate London dinner parties until Christmas. From an early preview, its spell is as seductive and sombre as ever.

First aired in Britain in early 2011, the tortuous 20-part crime serial went on to gain more viewers than Mad Men, creating an audience for subtitled TV drama and turning detective Sarah Lund into a modern icon. If the response confounded TV executives, it has amused the show’s star, Sofie Gråbøl, a veteran of the Copenhagen stage who still hasn’t adjusted to her British fame.

“It’s done very well in a lot of different countries, but nowhere has Lund been embraced like she has in Britain,” she says. “What is that about?”

A lot of it has to do with Gråbøl. When we meet she is a little hungover from a cast party the night before. “I really feel my 44 years today,” she says in a crooked Danish accent, though in fact she is shiny-eyed and radiant, in contrast to the hyper-intense, not always hyper-competent detective she portrays.

I posit my theory that it’s Lund’s intense relationship with her job that struck a chord with Londoners – particularly working women. She believes there’s more to it than that. “It’s a calling with her. It’s more like a vocation.

“When you think of Lund, she’s not a very sympathetic person,” she says. “Would you want to spend an evening with her? I don’t think so! She lets everyone down, she’s a terrible mother – she’s not really there for anyone. But she’s there for herself. She’s true to her very inner core. That’s why I, at least, forgive her everything.”

She is only just learning to let go of the character, who has been with her for the past seven years. Filming concluded only a few weeks ago, giving the storyline a fresh topicality (audiences in Britain, having caught the series five years after Denmark, are now almost up to speed). The financial crisis looms large in a saga that begins with the brutal murder of a sailor, expands to take in the disappearance of a billionaire’s young daughter and soon draws in the Prime Minister of Denmark himself.

Poor Lund – still heavy with heartache from series two – is trying to lead a quieter life and at first refuses to be drawn into the case. The viewer is caught in a classic bind. Do we want Lund to retain her sanity? Or do we want her to go nutzoid and solve the crime? The two seem mutually exclusive with Lund, though Gråbøl reckons that obsession is her version of contentment. “As long as you get lost in it – I think that’s very close to happiness. It’s the same thing with love, that feeling of being lost in another person, or, in Sarah Lund’s case, in a murder case.”

The filming process is similarly intense. The series creator, Søren Sveistrup, only hands over his scripts on Friday evening — shooting begins on Monday. “And that’s before the rewrites,” says Gråbøl, rolling her eyes. “It’s stressful. There’s no preparation time because the scripts aren’t finished. So, I must say, it’s been challenging and fun and dreadful.”

According to Sveistrup, it could not be done any other way. He originally created the series for the Danish station DR1 back in 2006, partly out of frustration at the competition. “I really think that a lot of television stinks,” he says. “Sometimes it feels like a competition of being stupid. I don’t get it. It’s made by intelligent people — so why don’t they make an effort?”

He set himself high ambitions, drawing on Twin Peaks and 24 for the first series. The third series was, everyone involved agrees, the most fraught. With most of the filming done at night, it also made childcare “ridiculous” for Gråbøl, a single mother with two small children. “When you say it’s been emotional, it has been emotional in a lot of ways. It was, and it has been, like a divorce for me. It has been a mix of sorrow and relief.” She burst into tears on the final day of shooting.

I ask her why so many Scandinavian shows have been hits over here – in the wake of The Killing we have had the political drama Borgen and the Swedish-Danish crime serial The Bridge. “In Denmark we’ve always felt related to you,” she says. “You just haven’t recognised us. Our tradition of telling stories is very similar. You have a fine tradition of crime telling — we always looked up to that. Once you’d discovered that you could get into a story even if you didn’t understand the language, I think you just discovered what the Danes have always known. It seems like the British people have been fascinated not only by the whodunit, but by our language, our architecture, our furniture… Who are these people? It’s really important that we exchange these stories, because we exchange who we are.”

Still, it is worth asking what DR1 — the Danish state broadcaster — does that the BBC could learn from. For Piv Bernth, the head of drama at the channel, which has also produced Borgen, it lies in putting the writer at the centre. “We really protect the idea of a single vision. The writer and producer are at the head of every show. The writer often gets lost in a TV show, but they don’t with us.”

The next series to look out for, she says, is called The Legacy, a family drama about a hippie-era artist who dies and leaves everything to the daughter she gave up for adoption, to the anger of the three other children. “The important thing is to keep what we do that’s special. If we try to make programmes like you do it, or the Americans do it, we’re lost,” says Bernth. “Our main target will always be the Danish audience.”

But Sveistrup clearly has his sights beyond Denmark. “I don’t compete with Danish shows. I compete with your shows and American shows,” he says. He has ruled out Hollywood. “I’m too stubborn. I don’t respond well to people telling me how to write.” But London? “Maybe London could be good… maybe one day — why not?”

And Gråbøl? She is currently performing in an adaptation of Ingmar Bergman’s Fanny and Alexander in Copenhagen and will soon be reunited with her former sidekick Jan Meyer (aka Danish actor Søren Malling, also in Borgen) in the Danish film I Lossens Time. One would assume British casting agents are calling? “From time to time,” she smiles. “Really, the last year-and-a-half, my schedule has been so packed that I haven’t been able to do the things that were offered. But next year it looks like there could be holes, so if the right project turns up, it would be great.”

Ah, wouldn’t it?

HOW TO BE A GREAT DANE ON KILLING NIGHT

Are you a Lund-head? Do you suffer from Danemania? If so, here’s our guide to everything you’ll need for The Killing’s return on Saturday night.

What to eat: You won’t have time to forage for wild horse mussels like Copenhagen-based Noma chef René Redzepi, so stick with Baltic herring, any kind of salmon, and even rare roast beef. Serve with dark rye bread. Avoid Lidl’s new frozen Siberian reindeer leg steaks, which have had negative reviews and may upset the children. Lund herself is impervious to good food and usually eats takeaways.

What to drink: The new limited- edition Tuborg Christmas Beer. It’s a major tradition in Denmark and has only just been released. “Danes are crazy for it. It’s a darker lager with a fuller taste and sweet undertones,” says Bronte Aurell, of Scandinavian Kitchen, which imports it.

What to read: The Killing Handbook. Written by actress and Celebrity Masterchef-turned-Forbrydelsen fanatic Emma Kennedy, this includes the lowdown on everything from the plot twists from series one to instructions for a Knit Your Own Sarah Lund. Seriously stalkerish. Alternatively, How to be Danish by Patrick Kingsley, who spent a month in Copenhagen earlier this year. More of a general guide.

What to wear: That sweater, obviously. Gudrun & Gudrun, creators of the cult woolly, are selling them online at 280 euros each. Alternatively, knit your own; you’ll find the pattern and instructions in The Killing Handbook.

Where to get it all: Scandinavian Kitchen, 61 Great Titchfield Street, W1. Emma Kennedy and Patrick Kingsley will also be signing books from 6-8pm tonight. Mulled wine will be served.